President Kennedy, in the months before his death, established the Presidential Medal of Freedom, and on Wednesday President Obama awarded this highest civilian honor to President Clinton, among other notables, including Oprah Winfrey, feminist leader Gloria Steinem, and country music singer Loretta Lynn. Later that day, the Obamas and the Clintons visited the Kennedy gravesite to pay homage to the forever young president 50 years after he was struck down.

“Obama was supposed to be our Kennedy, but that’s all gone. We don’t think of him that way anymore. What happened?” a young man asked historian Robert Dallek on his recent book tour to promote his latest volume on JFK. “It’s the natural erosion for anybody who’s there for eight years,” Dallek said. “If Kennedy had lived and had a second term, I’d be standing here today talking about the problems he’s facing.”

Those who love Kennedy imagine that his wit and charm and intellect would have carried him through the crises, and that he would have had the wisdom and the courage to spare the country the agony of Vietnam. But if Dallek is right, even JFK’s considerable gifts may not have been enough to stave off the second-term onslaught amply documented in the history books for those who win reelection.

Obama now is at the nadir of his presidency, and as he and Clinton stand together at Arlington Cemetery, each of them must be bothered in his own way at how intertwined their fate and fortunes are. For Obama, he’s the president who forged the coalition that could carry Hillary Clinton to the White House, and her husband is always upstaging him. Maybe Clinton meant no harm last week when he said Obama should keep his promise about letting people keep their health-insurance policy if they like it. But Clinton doesn’t let his mouth run without his brain being engaged, and it sure looked as if he was distancing Hillary from Obamacare, and maybe getting in a little dig at the same time.

Fair enough for Clinton to return the favor, after Obama was quoted in a new book saying he liked the former president “in small doses” following a lengthy golf game filled with conversation and too many mulligans for Obama’s taste. The problem is Clinton doesn’t come in small doses, and he “sees Obama making such stupid mistakes. He wonders, When will he learn how to play the game?” says a former aide to Vice President Biden.

Clinton made his share of stupid mistakes, too, says Sam Popkin, a political scientist and author of The Candidate: What it Takes to Win (and Hold) the White House. “It must gall Obama that Clinton had the chutzpah to blame him when he got something signed and Clinton never even got a vote on health care.” Still, Obama’s admission that he was unaware of the troubles plaguing HealthCare.gov before the website’s launch reveals his weakness as someone exercising oversight of the process. “‘Nobody told me’ is an incredibly damning statement. It means ‘I never asked,’” says Popkin.

For now, Hillary Clinton is a bystander, at the mercy of forces she can’t control. What’s at stake is her husband’s legacy, Obama’s presidency, the contours of her campaign, and the message she develops beyond breaking the glass ceiling, which is nice but insufficient. “If she runs, she will be held accountable for both the Clinton and Obama years, and she’ll have to forge a new identity,” says Jack Pitney, professor of politics at Claremont-McKenna College.

“From Hillary’s point of view, this is a romance novel, and she’s torn between her two men,” says Paul Equale, a Washington lawyer and longtime Democratic activist. There have always been simmering tensions between the Obama and Clinton camps, especially at the staff level, and the next three years will test all the players’ resilience and ability to compartmentalize. The assumption is that Bill Clinton is the least disciplined, but his wife’s tenure as secretary of state proved that he can resist the improvident remark when necessary. “His role for Hillary is to say the things she politically can’t. He is free to speak; she is far more circumspect,” says Equale.

At the risk of over-thinking Bill Clinton’s prodding of Obama on health care, it did give the former president a chance to vent. “But he needs to watch his venting,” says Pitney. “He doesn’t want Obama turning on Hillary,” not with Biden waiting eagerly in the wings. It’s hard to imagine open warfare breaking out between these two political families, not with so much to lose, but Pitney points out there are lots of ways to undercut another politician without making headlines, and the next months and years will bring fresh opportunities.

For now, Clinton is popular, a Democratic icon, and Obama is relying on him for a life raft in the current storm. Clinton knows something about comebacks, and if Obama can recover, Hillary is the beneficiary. Clinton can’t say it, not yet, but he thinks Hillary will be a better president than Obama, heck, maybe better than he was. As they stand by JFK’s grave, who knows what they’ll be thinking, but it might be a variation on Ben Franklin’s maxim, “We must all hang together, or assuredly we shall all hang separately.”